Let \(\lbrace \varepsilon _1, \ldots , \varepsilon _n\rbrace \)  be the canonical basis of the free abelian group \({\mathbb {Z}}^n\) .
In Bourbaki's notation the root system of type \(C_n\)  consist of the following elements (see [1]}):
the elements \(\pm \varepsilon _i\pm \varepsilon _j\)  (\(1\le i,j\le n\) , \(i\ne j\) ) are the short roots and
\(\pm 2\varepsilon _i\)  (\(1\le i\le n\) ) are the long roots.
